A generalized biquad with a programmable boost and natural frequency is often used in continuous time filter applications. In particular, read/write channels for hard drives utilize integrated continuous time filtering on CMOS circuits. The stability of the cut-off frequency and boost of continuous time filters are among characteristics of an integrated filter. One popular method of constructing a generalized biquad is through the use of a Gm-C technique often used for signal processing applications in disk-drive read channels. CMOS Gm-C filters are useful for circuits involving high-frequencies.
The Gm-C technique allows for an in-circuit filter tuning with high speed and low power requirements. Typically, the transconductance is held constant while the capacitance is tuned in the circuit or the capacitance is held constant, while the transconductance is tuned. Often transconductance tuning is preferred due to a larger dynamic range and low distortion. By utilizing transconductance tuning, the corner frequency, fc, and the gain, Q, of the filter can be obtained solely by modifying the transconductance, Gm, of Gm cells in the circuit.
The transconductance is often modified by adjusting a tuning voltage and/or tail current. Transconductance is defined by the following equation:                     Eq        .                                   ⁢        1            ⁢              :            ⁢                           ⁢      Gm        =          I      V        ,where V is the input voltage and I is the output current of the Gm cell.
With NMOS transistors as Gm setting devices and the tail current held constant, the transconductance increases as the tuning voltage is increased. Similarly, the transconductance decreases as tuning voltage is decreased. For NMOS with the voltage held constant, the transconductance increases as the tail current is increases and the transconductance decreases as the tail current decreases.
Operation of a biquad, or other circuit in which Gm cells are utilized, is also affected by environmental factors, such as temperature, and manufacturing process tolerances. In order to account for these factors, proportional-to-absolute temperature current sources (PTAT sources) are often used. With PTAT techniques, a thermometer is embedded in a chip and the current sent to the Gm setting device(s) is delivered with respect to absolute temperature, i.e. a Kelvin based measurement, thereby adjusting the transconductance. This solution is problematic because the temperature dependency of the transconductance is not necessarily linear. Moreover, an exact mathematical representation of the effect of temperature on the transconductance is often not known.
The PTAT approach suffers from large variations against changes of environmental temperature and often requires an increase in a power supply voltage above the safe upper limit of the process. Additionally, the circuit is sensitive to noise in the substrate or other circuits.